We show that the Eigen model and the asexual Wright-Fisher model can be obtained as two different limit cases of a single stochastic model. This result is used to enlighten the mathematical similarities and differences among these two models.The two key concepts introduced with the Eigen model, the error threshold and the quasispecies, are not invalidated by these differences, so that they are naturally present also in population genetics models. According to this fact, we use the classical diploid mutation-selection equation and the single peak fitness approximation to obtain the error threshold for sexual diploids. Finally, we perform the same analysis in the asexual case and compare the results.